One-dimensional semimetal contacts to two-dimensional semiconductors

Two-dimensional (2D) semiconductors are promising in channel length scaling of field-effect transistors (FETs) due to their excellent gate electrostatics. However, scaling of their contact length still remains a significant challenge because of the sharply raised contact resistance and the deteriorated metal conductivity at nanoscale. Here, we construct a 1D semimetal-2D semiconductor contact by employing single-walled carbon nanotube electrodes, which can push the contact length into the sub-2 nm region. Such 1D–2D heterostructures exhibit smaller van der Waals gaps than the 2D–2D ones, while the Schottky barrier height can be effectively tuned via gate potential to achieve Ohmic contact. We propose a longitudinal transmission line model for analyzing the potential and current distribution of devices in short contact limit, and use it to extract the 1D–2D contact resistivity which is as low as 10−6 Ω·cm2 for the ultra-short contacts. We further demonstrate that the semimetal nanotubes with gate-tunable work function could form good contacts to various 2D semiconductors including MoS2, WS2 and WSe2. The study on 1D semimetal contact provides a basis for further miniaturization of nanoelectronics in the future.

This work is quite timely, as interest has grown recently in mixed-dimensional 1D/2D heterostructures. These devices have the potential for offering the ultimate device down-scaling paradigm without the need for epitaxial lattice matching. The electrostatic nature of these interfaces has not been explored in detail and there is a distinct lack of experimental reports on certain standard figures of merit, such as the contact resistance. This manuscript addresses some of these issues and proposes a fabrication procedure for making 1D/2D FETs with consistent electrical performance, which is a big advance for the field. In addition, the CNT contacts are shown to improve electron transport quite strongly in intrinsically p-type WSe2 while preserving high hole mobilities, showing promise for CMOS-like applicability. The novelty in this report is quite high, but some of the conclusions are not supported by the data. Below is a list of outstanding issues that need to be addressed before this paper can be published in Nature Communications: Major issues: 1. I have a strong impression that the authors buried the lede of their own paper. The key statement of this work appears at the end of the fabrication section on page 3: "The DOS of the CNT is small and almost constant between the two first van Hove singularities, which efficiently suppresses the metalinduced gap states (MIGS) in MoS2 and thus eliminates the Fermi level pinning." This is the reason why the choice of CNT as a contact material to the 2D semiconductor is a major conceptual advancement described this work. In the abstract and introduction, the authors seem to suggest that gating the contact area allows for improved current injection into the channel, and this is the only reason for better electrical performance. However, this statement would also be true for any 2D semiconductor contact to a TMD, and in some sense is also true for metal contacts. What is unique here is that the band structure and resulting DOS of the semi-metallic CNT suppresses the MIGS-like effect in TMDs. It's precisely the interaction of the 1D DOS of the electrode with the 2D DOS of the channel that allows for the engineering of this efficient contact interface. It's also the reason why mixed-dimensional heterojunctions should be studied more in the future by other groups. The authors should stress this in the introduction of their paper, as right now there seems to be nothing special about the choice of CNT vs other materials-such as graphene or Bi.
2. One claim that seems to crop up throughout the manuscript is that the van der Waals gap between a CNT and a TMD is "obviously" shorter than that between two arbitrary 2D materials. The authors claim that this also enables a higher current flow between the two materials, and affects the tunneling efficiency of electrons. There are several issues with the topic of the vdW gap in this paper that the authors need to address: a. It is not obvious at all why the vdW gap between a CNT and MoS2 is smaller than that between graphene and MoS2. The illustrations shown in Fig. S4 show what looks like VESTA images, with the CNT and graphene structures at some distance away from the top of the MoS2. However, this drawing can be made arbitrarily in the software to have such a separation and it is unclear what is different physically about these heterostructures. Is the claim here that the carbon atoms in the CNT structure somehow have a different vdW interaction with MoS2 than the exact same carbon atoms in the graphene lattice? Is this something to do with the hybridization of the carbon orbitals? The authors need to discuss this in detail before making such a claim. In addition, at the end of the Methods section, the authors state that: "The vacuum distance of at least 12 Å in the z direction was imposed to eliminate the interactions between the periodic images." Again, it is unclear here what this means and how this affects the vdW gap for the calculations. b. If this difference in the vdW gap is in fact real, can the claim really be made that a separation difference to MoS2 of 0.36 Å between a CNT and graphene seriously affects charge transport across the interface? Previous works have shown that vdW gaps as large as 1.5 Å can be fully neglected when modelling tunneling transport-see, in particular, the calculation in the Methods section of [1]. c. The authors' own data, in fact, do not support this argument. The vdW gap is clearly visible in the FIB cross-sections in Figs. 1b and S2 in-between the MoS2 layers, but is hard to discern between the CNT and the MoS2 in those same images and in the smeared EELS map. I understand it is difficult to obtain clean images of this interface, but right now the TEM images are unconvincing in supporting any arguments on the nature of the vdW gap.
3. It is possible that the SBH extracted for the CNT/MoS2 interface may be convolved with the SBH of the CNT/Ti interface. Both the CNT/MoS2 and CNT/Ti junctions in this series resistor are gate-tunable and will show thermionic emission with a flat-band condition for electrons at some positive back-gate voltage (as the CNT is ambipolar and the MoS2 is n-type). The authors extract and compare the SBH of the CNT and Ti contacts on MoS2, but they do not provide a reference sample of SBH extraction on a CNT FET contacted with Ti only. This is quite necessary for extracting an absolute SBH value for the mixed-dimensional interface and proving that it is (or isn't) the current-limiting interface in this system. The Ti/CNT resistance is taken into account in the model derivation in later sections-as the R_nc^CNT and R_Q^CNT terms-and somehow plotted out in the inset of Fig. 3c, but there are no direct temperature-dependent flat-band experimental data confirming the SBH extraction for CNT/Ti in the same way as for the others. 4. The final outcome of the derived model is that the 1D/2D contact resistance achieved here is a function of the tunneling resistance (which is a non-trivial function of the separation) and the diameter of the CNT. But the CNT is a cylinder whose contact area with the MoS2 surface is likely much smaller than the diameter of the whole nanotube. Have the authors measured different diameters of CNTs as contacts to verify this model and to show that the contact resistance does in fact scale as 1/DCNT? It may be that the results are independent of diameter as only the tip of the CNT touches the MoS2 surface for all cases.
5. Details of the annealing procedure for removing the S particles from the CNT post-transfer need to be provided. Heat treatment in a sulfur environment may heal S vacancies in the MoS2 lattice and artificially improve electrical characteristics such as the mobility and transconductance. [2][3] The conditions of temperature, pressure, etc., need to be provided, and a comparison of the MoS2 electrical characteristics with and without annealing of the CNT contacts post-transfer should be shown to prove that it is not simply the annealing in close proximity to sulfur that improves the electrical performance of the MoS2 channel.
Minor issues: 6. Several works have been published in the last few years dealing specifically with TMD/CNT heterostructures. The introduction to this paper currently lacks any reference to works such as [4][5][6][7] to contextualize recent developments in 1D/2D mixed-dimensional devices and how this work improves on/is different from those previous publications.
7. On page 1: "In the case of traditional 3D metal, the average grain size is approximately equal to the smaller of the width and thickness". It's unclear what the authors are trying to say here. Perhaps a reference could be inserted here to help the reader get a better understanding of the effects of metal grain size on electrical contacts to 2D materials? 8. The authors often refer to their CNTs as being "ultralong", yet at no point in the paper or SI is it stated what the length of these CNTs actually is, and how this affects the transfer procedure with the W tips.
9. The green I-V curves in Fig. 4e are not described in the figure caption nor discussed in the main text at all. Fig. 3e says "drops sharply" when it actually increases sharply.

Caption of
11. Why does the MoS2 device in Fig. 4b have a negative threshold voltage when all previous MoS2 devices shown in the paper had a positive threshold voltage?
12. What is the reason for why the output characteristics don't saturate in Figs. 4c-e? In the case of low-SBH Bi contacts, TMD FETs can enter velocity saturation at much lower Vds values [8]. This might suggest the device behavior is still not channel-dominated here but rather contact-dominated by the CNT/Ti interface, as discussed above.
13. The variables DP, X and β in Fig. 3b are not discussed at all in the text or captions. 17. In the LTLM derivation in the SI, μm is sometimes written as um.
18. Some words in the boldface figure titles are often unnecessarily capitalized.
19. Some language mistakes crop up throughout, e.g., "no experimental exists", "electrodes that in contact with MoS2", "Fermi level of the intrinsic CNT located at its Dirac point", "and so as the SBH", etc.
[8] Shen, P.C., Su, C., Lin, Y., Chou, A.S., Cheng, C.C., Park, J.H., Chiu, M.H., Lu, A.Y., Tang, H.L., Tavakoli, M.M. and Pitner, G., 2021. Ultralow contact resistance between semimetal and monolayer semiconductors. Nature, 593(7858), pp.211-217 Reviewer #3: Remarks to the Author: In this work, a combinational experimental an theoretical study was performed on the transport properties of the semimetallic CNT-2D semiconductor interface. The authors reported measured 1D-2D contact resistivity value of 10^-6 Ohm cm^2, contact resistance value of 50 kOhm*um, Schottky barrier height of 191 meV. They further performed theoretical analysis and predicted that the contact resistivity and contact resistance can be much lower. The semimetal contact (with Bi and Sb) and CNT bundled contact for 2D semiconductors have been reported previously. Because of the bad band alignment between the CNT and MoS2 in this study, A Schottky barrier still exists even though a semimetal contact is used. This basically limits the contact resistance reduction as well as the device performance. The theoretical values predicted in this study did not take into consideration of the contributions from the Schottky barrier, so the prediction also needs to be adjusted. A somewhat new aspect of this study is that the contact length was reduced to ~ 1 nm, which may be important for a future ultimately scaled transistor technology.
Below are my additional questions/comments.
(1) The authors used the diameter of CNT as the contact length, but because the cross-sectional of CNT is round shape, the actual contact length might be much smaller than the diameter.
(2) it is not a fair comparison to use Ti/Au contact as the baseline, because Ti/Au contact is well known to be a very bad contact metal for TMDs. The author may need to consider using better candidates, such as Ni or Bi or Au (without Ti) as the control group.
(3) There is still a Schottky barrier at the CNT-MoS2 interface according to both the experimental results and the theoretical calculations. This means the selected CNT may not be a good choice for low-resistance contacts for TMDs. The authors may need to consider other types of CNTs or 1D semimetallic materials, which have lower work function to start with. (4) For the theoretical prediction about the contact reisistivity and contact reisistance, the authors missed an important term, which is the resistance contributed from the Schottky barrier height. After including this term, the predicated values may become much larger.

General Comments:
In the manuscript entitled "One-Dimensional Semimetal Contacts to Two-Dimensional Semiconductor", Li et al., report a novel junction contact between 1D-SWCNT and 2D-MoS2. This work presents some interesting and well-analyzed results. However, it seems to have a few issues to be considered before publication.

Response:
We thank Reviewer 1 very much for his/her kind and valuable comments on our manuscript. The suggestions are very helpful to improve the quality of our manuscript. We would like to address the concern below point-by-point. Supplementary experiments were also carried out to address the comments.  Here, we performed the annealing process under vacuum at 300 °C for 1h, which can achieve more complete desulfurization and form clean and tight van der Waals contact between CNT and TMD. It is technically challenging to measure the transfer curves of the suspended CNTs in fabrication processes ii and iii shown in Figure 1a. To confirm the desulfurization results experimentally, we fabricated a FET with a fresh semimetal CNT channel [PNAS 116, 6586-6593 (2019)]. Supplementary Fig. 5a shows the optical images of the device before sulfur deposition, after sulfur deposition and after annealing. It can be seen that there are no sulfur particles around the device after annealing treatment. Supplementary  Fig. 5b presents the corresponding transfer curves, in which the transfer curves of the CNT device before sulfur deposition and after annealing treatment almost coincide. But after sulfur deposition, the transfer characteristics of the CNT became gate-independent due to the doping of sulfur particles. These results indicate that the sulfur particles can be efficiently removed by the annealing treatment.   Fig. 5 Characterization of the effect of the sulfur deposition and annealing process on CNT. a, Optical images of a Ti-contacted CNT FET with semimetal CNT channel before and after sulfur treatment. Scale bar: 4μm. b, Transfer characteristics of the CNT FET before and after sulfur treatment. c, Raman spectra of the CNT before and after sulfur treatment.

Comment 2:
As MoS2 is very vulnerable to the temperature-dependent sulfur vacancy, the authors need to describe the desulfurization process of CNT in more details (including the environments like temperature, atmosphere, and time.). Also, to shoot out the defect issue of the MoS2, the authors need to provide clear evidences about the state of MoS2 via a comparative assessment between pre-/post-treated MoS2 samples.

Response 2:
We prepared a Ti/Au-contacted MoS2 FET to check whether the sulfur particles could contribute to the healing of vacancy in MoS2 by the annealing process. Supplementary Fig. 6a shows the optical images of the MoS2 FET before sulfur deposition, after sulfur deposition and after annealing. There are no sulfur particles around the device after annealing treatment. The Raman spectra of MoS2 in the three states ( Supplementary Fig. 6c) also show no significant differences. Supplementary Fig. 6b presents the transfer curves of the MoS2 FET corresponding to the three states. After sulfur deposition, the threshold voltage shits positively and the on current of the device decreases significantly, which is induced by the adsorption of sulfur particles. After annealing, the transfer curve of the device almost returns to the initial state. This is because the annealing procedure is carried out under vacuum (400 mTorr, Ar atmosphere), and it does not lead to a significant healing of sulfur vacancy compared with the high-pressure annealing process [3800 Torr, ACS Appl. Nano Mater. 3, 10462-10469 (2020)]. The actual amount of sulfur is decided by the sulfur particles attached on the transferred CNT, which is much less than that in this comparative experiment. Therefore, we can confirm that the sulfur-assisted CNT transfer technique does not affect the electrical properties of MoS2. These discussions have been added to the Supplementary Note 1. Supplementary Fig. 6 Characterization of the effect of the sulfur deposition and annealing process on MoS2. a, Optical images of a Ti-contacted MoS2 FET before and after sulfur treatment. Scale bar: 4μm. b, Transfer characteristics of the MoS2 FET before and after sulfur treatment. c, Raman spectra of the MoS2 before and after sulfur treatment.

Comment 3:
The RBM mode of CNT can span from ~130 cm -1 to ~300 cm -1 , depending on its van Hove electronic transition, size, and chirality, etc. However, it is difficult to evaluate this due to the breaking markers. The authors need to roll back the break regime. Like the author's statements, if the vdW gap between SWCNT and 2D MoS2 is so small, it is not suitable to monitor the posttransferred CNT solely. The authors need to proceed the comparative Raman study about both the pre-transfer suspended CNT and the post-transfer CNT in order to evaluate how RBM mode is influenced by the vdW interaction between them. If there occurred some shift due to the interaction, the current radius result on the transferred state can be modified somewhat.

Response 3:
We apologize for the incomplete wave number range shown in Figure 1d. The following Figure a shows the raw Raman spectra of the CNTs on Si/SiO2 substrate in range of 100 cm -1 to 400 cm -1 to confirm the RBM mode, which can also be found as Supplementary Fig. 4 in the revised supplementary materials. The RBM peaks around 146 cm -1 verify their single-walled structure and the same chirality of the two SWCNT electrodes. The prominent 303 cm -1 peak comes from the Si/SiO2 substrate, which is consistent with previous work [Phys. Rev. Lett. 86, 1118 (2001)]. As the signal from the substrate is much prominent than the signal from the SWCNTs, we set the breaking marker at 200 cm -1 , which keeps and highlights all the critical information from the CNT. As suggested by Reviewer 1, the RBM mode of SWCNT is affected by many factors, including the type of substrate, chirality of SWCNTs and et al. The structural determination of isolated SWCNT on Si/SiO2 substrate by resonant Raman scattering has been studied in Phys. Rev. Lett. 86, 1118 (2001). On Si/SiO2 substrate, the quantitative relationship between the RBM peak and SWCNT diameter can be expressed as = 248/ . Therefore, we measured the Raman spectra of CNTs on the Si/SiO2 substrate in our experiments (the red point in the following Figure

Comment 6:
In Figure 2f, the decay rate difference of ΦB between the two curves seems to be very similar in the high bias regime (Vg > 15 V). On the other hand, its bias-induced reduction is pretty remarkable in the lower bias regime (Vg < 10 V). Thus, CNT-effect seems to play a more dominant role in lowering the barrier in the low bias regime than in the higher bias regime. It would be better to check if the CNT/MoS2 sample follows the Square-root-type behavior of SWCNT work function as reported by Yu et al. (Nano Letters 9, 3430 (2009)).

Response 6:
We have added a detailed discussion on the dependence of the Sm-S interface barrier on Vg in the Supplementary Note 5. In summary, the SBH at the CNT/MoS2 interface can be efficiently modulated because of the absence of Fermi level pinning and the gate-tunable work function of CNT. The SBH can be reduced to zero and Ohmic contact can thus be achieved. The potential barrier at CNT-MoS2 interface is determined by the energy difference between the work function and affinity of MoS2 (Supplementary Figure 14a and Figure 15e). That is, the modulation is assisted by the tuning efficiency of MoS2's Fermi level, which is more efficient at lower Vg than at higher Vg. When the device is in the off state or subthreshold region, the potential barrier changes linearly with Vg, as the Fermi level of MoS2 is located in the band gap and the quantum capacitance of MoS2 equals 0; when the device is in the on state, the tuning efficiency of the barrier decreases significantly due to the increased quantum capacitance of MoS2 near the band edge. The Ti contact prepared by electron beam evaporation in our comparative experiments will damage the MoS2 in the contact area, resulting in additional surface states and may reduce the tuning efficiency of the barrier in the low bias regime.
Since "It can be seen that the at CNT-MoS2 interface changes significantly in the lower Vg regime and the tuning efficiency of the barrier decreases at higher Vg." "In addition to SBH, the modulation is also assisted by the tuning efficiency of MoS2's Fermi level, which is more efficient at lower Vg than at higher Vg (See details in Supplementary Note 5). Supplementary Fig. 15e Band diagrams of the CNT/MoS2 heterostructure under different Vg after junction formation.

Comment 7:
As shown in the CNT-contacted sample of Figure 2d, the current in the Vg-region lower than 35 V decreases with decreasing temperature (Vg < 35 V insulating), while it increases with temperature for the higher bias region (Vg > 35 V metallic). The insulating and metallic properties are related to the barrier height in the corresponding voltage regimes of Figure 2f. That is, the insulating property lasted until the barrier height reaches zero. So does Ti-contacted case in Figure 2d. However, in Figure S7, although the barrier height is nearly 0 eV above 40 V, the current increases with temperature in the overall voltage regime.

Response 7:
Many thanks to Reviewer 1 for carefully reading the manuscript and pointing out this contradiction. After carefully checking the experimental records and the previous versions of the manuscript, we find that the data in Supplementary Figure 7d is from a device with a 12-nm-thick MoS2 channel not a monolayer one. It is the smaller band gap of the thicker MoS2 that enables the insulator-metal transition at lower Vg. We apologize for mixing up the data from different samples and the data in the revised Supplementary Figure 13d has been corrected.
Comment 8: In Figure S4, the authors need to explain why the vdW gap of 3.08 Å comes out. Is the vdW gap value independent to the chirality of SWCNT? Can this small gap value be obtained only in the CNT with (5,5)?

Response 8:
The heterostructure shown in the Supplementary Figure 7a in the revised manuscript is the most stable structure with the lowest relative energy. The relative energy as a function of vdW gap is plotted in Supplementary Figure 7b. Moreover, the (5,5), (9,0) and (4,6) CNTs with the similar diameter were considered to examine the change of vdW gap. As shown in Supplementary Fig. 8 . Assume that the difference between the CNT contact and Graphene contact only lies in the barrier width, that is, the barrier width wt,Gr and barrier height Φt,Gr are 2.23 Å and 4.03 eV, respectively. The calculated tunneling resistivity of electrons is rt,Gr = 6.128×10 -9 Ω·cm 2 . Since the tunneling probability of electrons increases exponentially with the barrier width, the separation difference to MoS2 of 0.36 Å makes the tunneling resistivity of the Graphene contact more than double that of CNT contact. In general, the interface contact resistivity as low as 10 -9 Ω·cm 2 makes CNT and Graphene both good contact materials to 2D semiconductors (in Ohmic mode). In contrast, the CNTs with quasi-1D single crystal structure are the best-performance nano-scale quantum wires, while the graphene owns better current carrying capacity.
Revisions in the manuscript: 1. We have made revisions in the 3 rd paragraph of the Fabrication, characterization and DFT calculation of 1D semimetal contact section. "Since the tunneling probability of electrons increases exponentially with the barrier width, the smaller vdW gap indicates a smaller tunneling resistance." 2. We have made revisions in the last paragraph of the LTLM and extraction of contact resistance section. "Overall, in short contact limit, the 1D semimetal contact using individual SWCNT is prominent over most of the conventional metal contacts as well as the family of semimetal carbon nanomaterials including graphene and CNT bundles. Such performance can be attributed to the Ohmic contact achieved by gate modulation, the smaller vdW gap between 1D and 2D materials, and the perfect quasi-1D single crystal structure of CNT electrodes." Comment 10: The author described the longitudinal transfer length method (LTLM) method to estimate the contact resistance of between CNT/MoS2 channel. The equivalent circuit model was well designed, and the most of parameters used in calculation were also well measured, separately.
However, I am concerned about the measurement of . The authors mentioned that the was measured at the device in the orange box of Figure 1c. Since the CNTs are placed on the MoS2, the measured current can be influenced by the MoS2. How can the authors be sure that the measured current shows only the resistivity of CNTs?
Response 10: The influence from underlying MoS2 is neglected in the LTLM, which is reasonable and has been successfully applied in the resistivity comparison methodology to measure the resistivity of the semimetals that in contact with semiconductors [PNAS 119, e2119016119 (2022)]. Intuitively, the resistivity of semiconductors is much larger than that of metals. Furthermore, more evaluations were carried out on such systems. The resistance of a semimetal SWCNT, 1 μm in length, is about 4kΩ. The resistance experienced by the current flowing through MoS2 is over 1MΩ, which is about 3 orders of magnitude larger than the CNT resistance.

Revisions in the manuscript:
We have made revisions in the 3 rd paragraph of the LTLM and extraction of contact resistance section. "Since the current flowing through MoS2 is three orders of magnitude smaller than that in CNT, the influence of MoS2 can be neglected (electrodes A and E)."

Comment 11:
The authors mentioned that the Fermi level pinning at the CNT/MoS2 contact is suppressed by small DOS of the CNT. However, since CNTs were transferred onto MoS2, the interface between the two materials form a van der Waals contact. Therefore, the suppression of pinning might be due to the van Waals gap between the MoS2 and CNT (Nature 557, 696-700, (2018)). "Benefiting from the clean and intact vdW interface as well as the small DOS of CNT, the CNT electrodes perform well as ultra-short contacts for 2D MoS2 FET." Comment 12: In case of the 1D semimetal contact, author explained that injection efficiency of electrons from electrode to channel is greatly improved, and the contact resistance at the short contact limit shall be expressed as Rc = rc/DCNT. According to this expression, it is likely that CNT with a diameter larger than 2nm is better for improving the contact properties. Is there any experimental data using CNT with various diameter?
Response 12: As stated by Reviewer 1, the smaller contact resistance Rc should be obtained using larger diameter CNT for the larger contact length. However, the narrower CNT brings the unique ultrashort contact length as well as the Ohmic contact achieved by gate modulation at the same time, which cannot be reached by conventional top-down method. We have shown the experimental data using CNT with two different diameters in the manuscript. The diameter of the CNT used in the 4L-MoS2 FET was 1.7 nm and the diameter of the CNT used in the 1L-MoS2 FET was 1.5 nm (as shown in the AFM images in Supplementary Fig. 3). The calculated interfacial contact resistivity rc of them tends to be consistent in the Ohmic mode. However, it is a challenge to experimentally verify this principle in a wider range of the CNT diameter. First, it is limited by the CNT materials we have. The typical diameters of the as-grown ultralong single-walled CNTs are mostly in the range of 1 nm to 2 nm. The CNTs with larger diameters are always multi-walled, which complicates the carrier transport in CNTs. Furthermore, the resistance induced by the scattering at the junctions between the CNT wire on SiO2 and CNT contacts on MoS2 cannot be neglected anymore due to the nonlinear dispersion relationship of the multi-walled CNTs [Phys. Rev. Lett. 83, 5098-5101 (1999)]. This will prevent us from accurately extracting the interface contact resistance of CNT/MoS2. Second, the efficient 1D semimetal contact is contributed by both the 1D geometry and its electronic properties. The wider the diameter, the smaller the energy difference between the two first van Hove singularities. For example, the energy difference of (12, 12)-SWCNT (1. Moreover, the DOS of MWCNT is the sum of the DOS of each wall, the large semimetal DOS will reduce the tuning efficiency of the CNT work function as well as the contact performance.
We thank Reviewer 1 again for his/her kind and valuable comments, which have improved the quality of our manuscript.

--------------------------------Response to Reviewer 2 --------------------------------
General Comments: The paper by X. Li and colleagues reports on the electrical characteristics of 2D semiconductor FETs, e.g., MoS2, WSe2, contacted directly with semi-metallic carbon nanotubes as source and drain electrodes. The authors describe an involved fabrication procedure, perform DFT calculations to estimate the electrostatic nature of the CNT/MoS2 interface, and report the experimental transfer and output characteristics of several devices. The performance of the 2D FETs is notably improved when using CNT contacts vs traditional 3D metal contacts and the authors attribute this to the tunability of the CNT work function by the back-gate in the contact region. They derive a longitudinal transmission line model to extract resistivity parameters in their devices and claim record-low values for the contact resistance for this aggressively down-scaled contact region. This work is quite timely, as interest has grown recently in mixed-dimensional 1D/2D heterostructures. These devices have the potential for offering the ultimate device down-scaling paradigm without the need for epitaxial lattice matching. The electrostatic nature of these interfaces has not been explored in detail and there is a distinct lack of experimental reports on certain standard figures of merit, such as the contact resistance. This manuscript addresses some of these issues and proposes a fabrication procedure for making 1D/2D FETs with consistent electrical performance, which is a big advance for the field. In addition, the CNT contacts are shown to improve electron transport quite strongly in intrinsically p-type WSe2 while preserving high hole mobilities, showing promise for CMOS-like applicability. The novelty in this report is quite high, but some of the conclusions are not supported by the data. Below is a list of outstanding issues that need to be addressed before this paper can be published in Nature Communications:

Response:
We thank Reviewer 2 very much for his/her kind and valuable comments on our manuscript. We would like to address the concern below point-by-point. Supplementary experiments were also carried out to address the comments. Comment 1: I have a strong impression that the authors buried the lede of their own paper. The key statement of this work appears at the end of the fabrication section on page 3: "The DOS of the CNT is small and almost constant between the two first van Hove singularities, which efficiently suppresses the metal-induced gap states (MIGS) in MoS2 and thus eliminates the Fermi level pinning." This is the reason why the choice of CNT as a contact material to the 2D semiconductor is a major conceptual advancement described this work. In the abstract and introduction, the authors seem to suggest that gating the contact area allows for improved current injection into the channel, and this is the only reason for better electrical performance. However, this statement would also be true for any 2D semiconductor contact to a TMD, and in some sense is also true for metal contacts. What is unique here is that the band structure and resulting DOS of the semi-metallic CNT suppresses the MIGS-like effect in TMDs. It's precisely the interaction of the 1D DOS of the electrode with the 2D DOS of the channel that allows for the engineering of this efficient contact interface. It's also the reason why mixed-dimensional heterojunctions should be studied more in the future by other groups. The authors should stress this in the introduction of their paper, as right now there seems to be nothing special about the choice of CNT vs other materials-such as graphene or Bi.
Response 1: Many thanks to Reviewer 2 for this valuable comment. We have revised the introduction in the manuscript and the band diagrams in Figure 2g, Figure 3d and Figure 4a to address this comment.
Revisions in the manuscript: 1. We have added a discussion to emphasize the uniqueness of the 1D semimetal SWCNT in the 2 nd paragraph of the introduction section. "Recent progress has shown that they can be assembled with 2D materials to form mixed-dimensional vdW heterostructures with multiple functions. Furthermore, the density of states (DOS) of the 1D semimetal SWCNT is small and almost constant between the two first van Hove singularities. In such semimetal-semiconductor junctions, the clean and intact vdW interface as well as the suppressed metal-induced gap states (MIGS) in semiconductors can effectively eliminate the Fermi level pinning. The small DOS could also enable an efficient modulation on work function of CNTs by external electric field. Therefore, the gate-tunable Schottky barrier height (SBH) at such 1D/2D interface can be predicted. All these specific properties indicate that the individual semimetal SWCNT has great potential as an ultimate scaled contact in 2D electronics." 2. We have replaced the Dirac cones in Figure 2g, Figure 3d and Figure 4a with the DOS diagram to emphasize the 1D electronic structure of the semimetal SWCNT.

Comment 2:
One claim that seems to crop up throughout the manuscript is that the van der Waals gap between a CNT and a TMD is "obviously" shorter than that between two arbitrary 2D materials. The authors claim that this also enables a higher current flow between the two materials, and affects the tunneling efficiency of electrons. There are several issues with the topic of the vdW gap in this paper that the authors need to address: a. It is not obvious at all why the vdW gap between a CNT and MoS2 is smaller than that between graphene and MoS2. The illustrations shown in Fig. S4 show what looks like VESTA images, with the CNT and graphene structures at some distance away from the top of the MoS2. However, this drawing can be made arbitrarily in the software to have such a separation and it is unclear what is different physically about these heterostructures. Is the claim here that the carbon atoms in the CNT structure somehow have a different vdW interaction with MoS2 than the exact same carbon atoms in the graphene lattice? Is this something to do with the hybridization of the carbon orbitals? The authors need to discuss this in detail before making such a claim. In addition, at the end of the Methods section, the authors state that: "The vacuum distance of at least 12 Å in the z direction was imposed to eliminate the interactions between the periodic images." Again, it is unclear here what this means and how this affects the vdW gap for the calculations. b. If this difference in the vdW gap is in fact real, can the claim really be made that a separation difference to MoS2 of 0.36 Å between a CNT and graphene seriously affects charge transport across the interface? Previous works have shown that vdW gaps as large as 1.5 Å can be fully neglected when modelling tunneling transport-see, in particular, the calculation in the Methods section of [1]. c. The authors' own data, in fact, do not support this argument. The vdW gap is clearly visible in the FIB cross-sections in Figs. 1b and S2 in-between the MoS2 layers, but is hard to discern between the CNT and the MoS2 in those same images and in the smeared EELS map. I understand it is difficult to obtain clean images of this interface, but right now the TEM images are unconvincing in supporting any arguments on the nature of the vdW gap.
Response 2: a. The heterostructure shown in the Supplementary Figure 7a in the revised manuscript is the most stable structure with the lowest relative energy. The relative energy as a function of vdW gap is plotted in Supplementary Figure 7b. The smaller vdW gap should come from the 1D geometry structure of CNT, which induces a reduced equilibrium distance between the 1D CNT and 2D MoS2. In Methods section, the vacuum distance of at least 12 Å in the z direction was imposed to eliminate the interactions between the periodic images. As shown in the Figure bellow, a 1 × 3 × 2 supercell of CNT/MoS2 heterostructure is presented. It can be seen that the vacuum distances along y and z direction are 10 and 12.5 Å, respectively, which avoid the interaction between CNTs and CNT/MoS2 heterostructures of adjacent period. For low dimensional (0D, 1D and 2D) system, this vacuum distance is essential in theoretical calculations.

b.
We have evaluated the tunneling resistivity at the Ohmic CNT/MoS2 and Graphene/MoS2 interfaces. According to the updated DFT calculation results, the CNT/MoS2 heterojunction achieves Ohmic contact under the positive electric field of 0.2 V/Å. The corresponding barrier width wt and barrier height Φt are 1.87 Å and 4.03 eV, respectively. And the calculated tunneling resistivity of electrons is rt = 2.882×10 -9 Ω·cm 2 . Assume that the difference between the CNT contact and Graphene contact only lies in the barrier width, that is, the barrier width wt,Gr and barrier height Φt,Gr are 2.23 Å and 4.03 eV, respectively. The calculated tunneling resistivity of electrons is rt,Gr = 6.128×10 -9 Ω·cm 2 . Since the tunneling probability of electrons decreases exponentially with the barrier width, the separation difference to MoS2 of 0.36 Å makes the tunneling resistivity of the Graphene contact more than double that of CNT contact. In 2018, Liu et al., reported that the highquality vdW integration of metals and 2D semiconductors effectively suppresses the Fermi level pinning, making the SBH at the metal-semiconductor interface close to the Schottky-Mott limit [Nature 557, 696-700, (2018)]. The Schottky barrier exist at the metal/semiconductor interface. Compared with the contact resistance caused by the Schottky barrier (10 -5 ~ 10 -3 Ω·cm 2 ), the electron tunneling resistance induced by the vdW gap is indeed negligible (10 -9 Ω·cm 2 ). This indicates that Ohmic contact and vdW contact are the two essential factors to achieve high performance contact to 2D semiconductors. c. The STEM and EELS images in Figure 1b and Supplementary Fig. 2 are used to confirm the CNT/MoS2 heterostructure, which is the best result we have got after many attempts. As stated by Reviewer 2, it is challenging to obtain the atomically sharp STEM image of the CNT-MoS2 interface experimentally, due to the poor electron beam tolerance and the single layered nanostructure of CNT. Therefore, we further use DFT calculation to effectively analyze the mixed-dimensional heterostructure.
Revisions in the manuscript: 1. We have made revisions in the 3 rd paragraph of the Fabrication, characterization and DFT calculation of 1D semimetal contact section. "To present the geometry and electronic structures of the mixed-dimensional heterojunction, density functional theory (DFT) calculations were performed on a (5,5) CNT/MoS2 heterostructure. The junction atomic structure, differential charge density and electrostatic potential distribution are presented in Figure 1e. Comparative calculations were also conducted on a graphene/MoS2 heterojunction (Supplementary Figure 7). As shown by the variation of the relative energy as a function of interlayer distance, the most stable structure shows a vdW gap of 3.06 Å for CNT/MoS2 and 3.42 Å for graphene/MoS2, respectively. The obviously small vdW gap of such 1D-2D junction can be attributed to CNT's tubular structure. Since the tunneling probability of electrons increases exponentially with the barrier width, the smaller vdW gap indicates a smaller tunneling resistance." 2. The relative energy as a function of vdW gap has been added as Supplementary Figure 7b in the revised manuscript. Supplementary Fig. 7 a, Top and side views of the CNT/MoS2 and graphene/MoS2 heterostructures. b, Relative energy of CNT/MoS2 and graphene/MoS2 heterostructures as a function of vdW gap. The CNT/MoS2 presents obviously smaller vdW gap due to the tubular structure of CNT.

Comment 3:
It is possible that the SBH extracted for the CNT/MoS2 interface may be convolved with the SBH of the CNT/Ti interface. Both the CNT/MoS2 and CNT/Ti junctions in this series resistor are gate-tunable and will show thermionic emission with a flat-band condition for electrons at some positive back-gate voltage (as the CNT is ambipolar and the MoS2 is n-type). The authors extract and compare the SBH of the CNT and Ti contacts on MoS2, but they do not provide a reference sample of SBH extraction on a CNT FET contacted with Ti only. This is quite necessary for extracting an absolute SBH value for the mixed-dimensional interface and proving that it is (or isn't) the current-limiting interface in this system. The Ti/CNT resistance is taken into account in the model derivation in later sections-as the R_nc^CNT and R_Q^CNT terms-and somehow plotted out in the inset of Fig. 3c, but there are no direct temperature-dependent flat-band experimental data confirming the SBH extraction for CNT/Ti in the same way as for the others.  Supplementary Figure 12c. Experimentally, we have supplemented the temperaturedependent transfer characteristics and output characteristics of the CNT devices in Supplementary  Fig. 12a and 12b. It can be seen that as the temperature decreases, the conduction current of the device increases, showing good metallicity and indicating that there is no potential barrier at the Ti/CNT interface. In the CNT-contacted MoS2 transistors, the contact resistance between Ti and CNT is = 2 + , where ~2 Ω is the interfacial resistance caused by the imperfect contact between Ti and CNT, = 6.5 kΩ is the quantum resistance determined by the number of conductive channels of CNT [Nature nanotechnology 5, 858-862 (2010)]. Thus, the ~10.5 Ω.
In contrast, the sheet resistivity of the 4L-MoS2 was measured as ρ 2D = 120 kΩ·☐ -1 at Vg = 50V, and the channel resistance of the device (L=9.2μm, W=3μm) equals 368 kΩ. Therefore, the contact resistance at the Ti/CNT interface is much smaller and it is not the current-limiting interface in this system.

Revisions in the manuscript:
The Supplementary Figure 12 has been added.
Supplementary Fig. 12 Temperature-dependent electrical transport properties of the semimetal SWCNT. The temperature-dependent transfer curves (a) and output curves (b) of the semimetal SWCNT. Inset is the SEM image of the CNT device. Scale bar: 2μm. The conductivity of semimetal SWCNT increases with the temperature decreases, showing good metallicity and indicating that there is no potential barrier at the metal/CNT interface. c, Band diagrams of the metal/CNT junctions before and after contact formation.

Comment 4:
The final outcome of the derived model is that the 1D/2D contact resistance achieved here is a function of the tunneling resistance (which is a non-trivial function of the separation) and the diameter of the CNT. But the CNT is a cylinder whose contact area with the MoS2 surface is likely much smaller than the diameter of the whole nanotube. Have the authors measured different diameters of CNTs as contacts to verify this model and to show that the contact resistance does in fact scale as 1/DCNT? It may be that the results are independent of diameter as only the tip of the CNT touches the MoS2 surface for all cases.

Response 4:
Considering the feature size of the contact geometry, we default that the contact length of the 1D semimetal contact is equal to the diameter of CNT. We have defined it in the revised LTLM and extraction of contact resistance section. "The contact length is defined as the diameter of CNT (the feature size of contact geometry)." However, the tubular structure of CNT makes things more complicated, as the actual contact length is probably smaller than the CNT diameter. It is an important scientific issue and should continue to be studied in depth. In experiment, we have shown the experimental data using CNT with two different diameters in the manuscript. The diameter of the CNT used in the 4L-MoS2 FET was 1.7 nm and the diameter of the CNT used in the 1L-MoS2 FET was 1.5 nm (as shown in the AFM images in Supplementary Fig. 3). The calculated interfacial contact resistivity rc of them tends to be consistent in the Ohmic mode. However, it is a challenge to experimentally verify this principle in a wider range of the CNT diameter. First, it is limited by the CNT materials we have. The CNTs with larger diameters are always multi-walled, which complicates the carrier transport in CNTs. Furthermore, the resistance induced by the scattering at the junctions between the CNT wire on SiO2 and CNT contacts on MoS2 cannot be neglected anymore due to the nonlinear dispersion relationship of the multi-walled CNTs [Phys. Rev. Lett. 83, 5098-5101 (1999)]. This will prevent us from accurately extracting the interface contact resistance of CNT/MoS2. On the other hand, the efficient 1D semimetal contact is contributed by both the 1D geometry and its electronic properties. The larger the diameter, the smaller the energy difference between the two first van Hove singularities. For example, the energy difference of (12, 12)-SWCNT (1.65nm) is 1.5 eV, while that of the (36, 36)-SWCNTs (4.95 nm) is only 0.5 eV [http://www.photon.t.u-tokyo.ac.jp/~maruyama/kataura/1D_DOS.html]. This limits the tunable range of the work function of the semimetal CNTs. Moreover, the DOS of MWCNT is the sum of the DOS of each wall, the large semimetal DOS will reduce the tuning efficiency of the CNT work function as well as the contact performance.
Comment 5: Details of the annealing procedure for removing the S particles from the CNT posttransfer need to be provided. Heat treatment in a sulfur environment may heal S vacancies in the MoS2 lattice and artificially improve electrical characteristics such as the mobility and transconductance. [2][3] The conditions of temperature, pressure, etc., need to be provided, and a comparison of the MoS2 electrical characteristics with and without annealing of the CNT contacts post-transfer should be shown to prove that it is not simply the annealing in close proximity to sulfur that improves the electrical performance of the MoS2 channel.

Response 5:
We prepared a Ti/Au-contacted MoS2 FET to check whether the sulfur particles could contribute to the healing of vacancy in MoS2 by the annealing process. Supplementary Fig. 6a shows the optical images of the MoS2 FET before sulfur deposition, after sulfur deposition and after annealing. There are no sulfur particles around the device after annealing treatment. The Raman spectra of MoS2 in the three states ( Supplementary Fig. 6c) also show no significant differences. Supplementary Fig. 6b presents the transfer curves of the MoS2 FET corresponding to the three states. After sulfur deposition, the threshold voltage shits positively and the on current of the device decreases significantly, which is induced by the adsorption of sulfur particles. After annealing, the transfer curve of the device almost returns to the initial state. This is because the annealing procedure = − are Schottky barrier height, the energy difference between the work function and affinity of the semiconductor, the surface potential of the semiconductor, respectively. For When the Fermi level of MoS2 is located in the band gap, the , = 0 and = − . Therefore, the is linearly correlated with Vg and the conduction current in the device increases exponentially (corresponding to the subthreshold region), which is consistent with the low Vg regime (Vg < 10V) in Figure 2a